First, the paired holes require some adjustment to the "cross number" used in the various spoke length calculators. But how much? Spocalc.xls says to increase the cross numbers relative to a normal wheel, e.g. for a 20 hole wheel w/ 2x lacing use 2.29 cross. That makes sense if the two spokes on one flange "tab" do not cross (like the front wheel in the example pictures above) but not if they do (like the rear wheel). How do I calculate the cross number adjustments?

Second, the flange cutouts are offset from each other left-to-right. How does this affect spoke length?

Well, Spocalc does paired spoke calculations based on the assumption that the hub's spoke holes are evenly spaced. What you need to do is figure out how many degrees apart the spoke holes are. Spocalc says this:

So I wrote a computer program to help me visualize the designs and understand. I learned a few things.

First, the angular offset of a pair of spoke holes on the left flange relative to the nearest pair on the right flange is determined only by spoke count N. It is independent of the angle between a pair of holes on the hub. A pair of holes on one side at 2π/N relative to the nearest pair on the other side.

Second, it turns out that Spocalc assumes, when it recommends fractional values of cross number X, that the two spokes in a pair of adjacent holes (on one side of the hub) do not cross each other. In other words, the two spokes are pulling on the flange material between the pair of spoke holes. This is why spocalc’s X for a paired-spoke-hole hub is larger than for a regular hub.

Let’s try to visualize this.

Start with X=1 for a regular one-cross lacing with uniform hole spacing.

Here we have a 20-spoke wheel with a small ERD and large hub PCD to help make the images clearer. Hub spoke holes on the front side, as we look at it, are black—on the rear they are green. Front leading spokes are orange, front trailing are red, rear leading are cyan and rear trailing are green.

Now get rid of the rear spokes and spoke holes for clarity.

Next, increase X to 1 < X < 1.5. The diagram shows X = 1.3.

It’s still a one-cross lacing but now the hub has paired holes, meaning that each J end of one spoke is closer to the J end of one neighbor than its other. But these “paired” spokes don’t cross.

Increase X again to 1.5 < X < 2 and now you have a two-spoke lacing—the two paired spokes cross each other. The diagram has X = 1.7.

These last two pictures are of the same hub. Spocalc is offering only the first lacing but I don’t see anything wrong with the second.

If you increase again to X = 2 then the pair move apart so that each hole is equally distant to both of its neighbors and you're back to a regular hub.

The third lesson is how X relates to the angle θ between a pair of spoke holes. θ = 4π/N when X is an integer. θ = 0 when X = 1/2 + an integer, e.g. X = 3/2, which is an impossible hub in practice. In general θ = 8π/N⋅abs(1/2 - frac(X)), which allows me to calculate X given measurements from the hub.